FM modulated waves used in FM radio broadcasting and television broadcasting are signals in which a sine wave carrier signal is subjected to phase modulation by a music signal. FM modulated waves have high resistance against noise and can transmit music signals having a broadband of 15 kHz with a low distortion factor.
However, in multipath propagation paths, which include paths other than the path by which a radio wave arrives directly and in which radio waves are reflected by obstructions such as buildings and thus arrive with a delay, the phase information required for demodulation is disturbed by the influence of strong reflected waves that are received together with direct waves, and distortion therefore occurs in the demodulated signal. This distortion that is produced as a result of multipath propagation paths is referred to as “multipath distortion.” An equalizer for reducing multipath distortion by correcting the characteristics of multipath propagation paths is referred to as a “multipath equalizer” or a “multipath distortion canceller.”
A multipath equalizer compensates for the effect of multipaths in a received signal by passing the received signal through a filter having the inverse characteristics of the multipath propagation paths, i.e., an inverse filter. The characteristics of the multipath propagation paths change according to the environment, and the characteristics of the inverse filter therefore must also be optimized according to the conditions over time. As a result, adaptive digital filters are typically used as inverse filters.
An adaptive digital filter is a filter having the capability for automatically updating the filter coefficient according to changes in the environment. An algorithm for calculating filter coefficients at each point in time is referred to as an “adaptive algorithm,” an LMS (Least Mean Square) algorithm being a representative example. In a broad sense, an LMS algorithm is a method of minimizing the root-mean-square error based on a steepest-descent method and offers the advantages of stability and a small amount of operations.
Adaptive algorithms known as complex LMS algorithm are also known. A complex LMS algorithm is an extension of the LMS algorithm in which each of the input signal, output signal, target signal, and filter coefficients are complex amounts, and is used, for example, when adapting reference signal by separating the in-phase component and quadrature component when the input is a narrow-band high-frequency signal.
On the other hand, a conventional equalizer that is realized by an adaptive digital filter requires a reference signal (training signal) for this adaptation, and this requirement tends to cause an interruption in communication and a reduction of communication efficiency due to redundant reference signals.
In contrast, a recently developed equalizer known as the “blind equalizer” performs restorative equalization of signals based only on the received signals without requiring a reference signal for adaptation. An algorithm for application in this type of blind equalization is called a “blind algorithm,” a CMA (Constant Modulus Algorithm) being a representative example.
As shown in Non-Patent Document 1, CMA typically refers to an algorithm in which a statistic relating to the output signal such as the envelope of the filter output or a higher-order statistic is taken as an index, the algorithm updating filter coefficients such that this index approaches a target value. When using a constant-amplitude modulated wave in which the amplitude of the modulated wave is fixed as in FM modulation, the envelope of the filter output, i.e., amplitude, is used as the index and the filter coefficients are updated to minimize the error between a target value and the value of the envelope of the signal following passage through the filter, as shown in Non-Patent Document 2. In this way, distortion of phase is also corrected together with the distortion of the envelope, and the influence of reflected waves of multipath propagation paths is eliminated.
Here, CMA is a different concept than an adaptive algorithm. In CMA, an adaptive algorithm such as the previously mentioned LMS algorithm is used as an adaptive algorithm for calculating filter coefficients at each time point.
In order to uniformly control the value of the envelope of the output signal of a filter as previously described, the value of the envelope must be extracted instantaneously, and complex signal processing is a representative method of this type of extraction. In complex signal processing, a real signal f2 having phase that is delayed 90° (π/2) with respect to a particular real signal f1 is generated by, for example, a Hilbert transformer, and a complex signal (typically referred to as an “analytic signal”) having f1 in a real part and f2 in an imaginary part is generated. In this way, the value of the envelope of this real signal can be found instantaneously by calculating the square sum of the real part and imaginary part of the complex signal. However, when the output signal of the filter is subjected to complex signal processing, delay caused by the complex signal processing enters into the coefficient update loop and gives rise to instability of the loop. As a result, the complex signal processing is carried out on the input signal. In such cases, the input signal becomes a complex signal, and an algorithm that can handle complex quantities such as a complex LMS algorithm is therefore used as the adaptive algorithm. This method is referred to as the “first technique of the related art.”
FIG. 1 shows the configuration of an adaptive digital filter that uses the first technique of the related art.
Referring to FIG. 1, input signal X(k) has been converted to a complex signal by a Hilbert transformer (not shown). Complex filter coefficient vector W(k) is convoluted by this complex signal as input to obtain output signal y(k), which is a complex signal. Complex filter coefficient vector W(k) is updated by an adaptive algorithm that has been expanded to handle complex signals such that the value of the envelope of output signal y(k) approaches a target value that has been prescribed in advance. The algorithm of this adaptive digital filter is represented as shown below:W(k+1)=W(k)−μ(|y(k)|p−yref0)qy(k)XH(k)  (1)y(k)=WT(k)X(k)  (2)W(k)=[w0(k),w1(k), . . . , wN−1(k)]T  (3)X(k)=[x(k),x(k−1), . . . , x(k−N+1)]T  (4)
where W(k) represents a filter coefficient vector, X(k) represents a complex signal vector, k represents a sample index, N represents the number of filter taps, y(k) represents the output signal, yref0 represents the envelope target value, and μ represents a parameter for determining the amount of update of the filter coefficients. In addition, H represents a complex conjugate transposition, and T represents a transposition. The values p and q are constants for determining an evaluation function of error for the envelope target value, and for example, may be p=1 and q=1.
In the first technique of the related art, two signals having phases that are shifted 90° (π/2) with respect to each other are generated by applying complex signal processing. However, as can be seen from Patent Document 1 and Non-Patent Document 3, if sampling is carried out at a frequency of (4/odd number) times the carrier frequency when sampling the input signal, the phases of adjacent sample points will be shifted 90°. By taking this approach, an adaptive algorithm for handling real numbers can be used as is, whereby the square sum of adjacent sample points can be calculated when seeking the value of the envelope of the output signal. This method is referred to as the “second technique of the related art.”
FIG. 2 shows the configuration of an adaptive digital filter that uses the second technique of the related art.
Referring to FIG. 2, input signal Xr(k) is a real signal, and the real-signal filter coefficient vector Wr(k) is convoluted by this real signal as input to obtain real-signal output signal yr(k). Filter coefficient vector Wr(k) is updated by an adaptive algorithm that handles real coefficients such that the envelope of output signal yr(k) approaches a target value that has been prescribed in advance. This adaptive digital filter algorithm is represented as shown below:Wr(k+1)=Wr(k)−μ(Env[yr(k)]−yref0)yr(k)Xr(k)  (5)yr(k)=WrT(k)Xr(k)  (6)Env[yr(k)]=(yr2(k−1)+yr2(k))1/2  (7)Wr(k)=Re[W(k)]  (8)Xr(k)=Re[X(k)]  (9)
where Wr(k) represents a real coefficient vector, Xr(k) represents a real signal vector, Env[ ] represents an operation for obtaining an approximate value of the envelope, Re[ ] represents an operation for taking the real part of the complex number, and yr(k) represents a real-number output signal.
However, in the adaptive digital filter shown in FIG. 1, nearly all signal processing, for example, for input signal X(k), filter coefficient vector W(k), and output signal y(k), is carried out by complex numbers. A single multiplication of complex numbers corresponds to four multiplications and two additions of real numbers. In a multipath equalizer for an FM receiver, convolution operations and coefficient updating operations of most filters having many taps must be executed for each short sampling period, and this raises the problem of a voluminous amount of operations.
In the adaptive digital filter shown in FIG. 2, on the other hand, if the sampling frequency is precisely (4/odd number) times the center frequency of an intermediate-frequency signal, the calculation accuracy of the envelope can be increased, the same performance as the adaptive digital filter of FIG. 1 can be obtained, and moreover, the operation load can be reduced to approximately 25%. Nevertheless, this technique suffers from the problems that the sampling frequency is subject to strict limits and design for any sampling frequency is not possible. If the sampling frequency is shifted from (4/odd number) times the center frequency of an intermediate frequency signal, the accuracy of calculating the envelope drops and the multipath equalization capabilities therefore deteriorate.    Patent Document 1: JP-A-2005-064618    Non-Patent Document 1: C. Richard Johnson, Jr., Philip Schniter, Thomas J. Endres, James D. Behm, Donald R. Brown, and Raul A. Casas, “Blind Equalization Using the Constant Modulus Criterion: A Review,” Proceedings of IEEE, Vol. 86, No. 10, October 1998.    Non-Patent Document 2: J. R. Treichler and B. G. Agee, “A New Approach to Multipath Correction of Constant Modulus Signals,” IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 31, No. 2, pp. 459-472, April 1983.    Non-Patent Document 3: Itami Makoto, Hatori Mitsutoshi, Tsukamoto Norio, “Hardware Implementation of FM Multipath Distortion Canceller,” National Convention Record of the Institute of Television Engineers of Japan, No. 22, pp. 355-356, 1986.